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a(n) = Product_{d|n} T(d) where T(x) = x*(x+1)/2 = A000217(x) = x-th triangular number.
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%I #11 Sep 08 2022 08:46:17

%S 1,3,6,30,15,378,28,1080,270,2475,66,294840,91,8820,10800,146880,153,

%T 2908710,190,5197500,38808,50094,276,3184272000,4875,95823,102060,

%U 35809200,435,17401230000,496,77552640,222156,273105,264600,1511016670800,703,422370,425880

%N a(n) = Product_{d|n} T(d) where T(x) = x*(x+1)/2 = A000217(x) = x-th triangular number.

%C Conjecture: the sequence is injective (all terms of this sequence occur only once).

%H Jaroslav Krizek, <a href="/A275786/b275786.txt">Table of n, a(n) for n = 1..1000</a>

%F a(p) = A000217(p) = p*(p+1)/2 for a prime p.

%e a(4) = 30 because the divisors of 4 are: 1, 2 and 4; and T(1)*T(2)*T(4) = 1*3*10 = 30.

%p f:= n -> convert(map(t -> t*(t+1)/2,numtheory:-divisors(n)),`*`):

%p map(f, [$1..100]); # _Robert Israel_, Aug 09 2016

%t t[n_]:=Divisors[n]*(Divisors[n]+1)/2;a[n_]:=Times@@t[n];Array[a,50] (* _Ivan N. Ianakiev_, Aug 15 2016 *)

%o (Magma) [(&*[d*(d+1) div 2: d in Divisors(n)]): n in [1..100]]

%Y Cf. A000217, A007437 (Sum_{d|n} T(d)).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Aug 09 2016